Generalized Linear Models  book cover
2nd Edition

Generalized Linear Models

ISBN 9780412317606
Published August 1, 1989 by Chapman and Hall/CRC
532 Pages

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Book Description

The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications.

The authors focus on examining the way a response variable depends on a combination of explanatory variables, treatment, and classification variables. They give particular emphasis to the important case where the dependence occurs through some unknown, linear combination of the explanatory variables.

The Second Edition includes topics added to the core of the first edition, including conditional and marginal likelihood methods, estimating equations, and models for dispersion effects and components of dispersion. The discussion of other topics-log-linear and related models, log odds-ratio regression models, multinomial response models, inverse linear and related models, quasi-likelihood functions, and model checking-was expanded and incorporates significant revisions.

Comprehension of the material requires simply a knowledge of matrix theory and the basic ideas of probability theory, but for the most part, the book is self-contained. Therefore, with its worked examples, plentiful exercises, and topics of direct use to researchers in many disciplines, Generalized Linear Models serves as ideal text, self-study guide, and reference.

Table of Contents

The Origins of Generalized Linear Models
Scope of the Rest of the Book
An Outline of Generalized Linear Models
Processes in Model Fitting
The Components of a Generalized Linear Model
Measuring the goodness of Fit
An Algorithm for Fitting Generalized Linear Models
Models for Continuous Data with Constant Variance
Error Structure
Systematic Component (Linear Predictor)
Model Formulae for Linear Predictors
Tables as Data
Algorithms for Least Squares
Selection of Covariates
Binary Data
Binomial Distribution
Models for Binary Responses
Likelihood functions for Binary Data
Models for Polytomous Data
Measurement scales
The Multinomical Distribution
Likelihood Functions
Log-Linear Models
Likelihood Functions
Log-Linear Models and Multinomial Response Models
Multiple responses
Conditional Likelihoods
Marginal and conditional Likelihoods
Hypergeometric Distributions
Some Applications Involving Binary data
Some Aplications Involving Polytomous Data
Models with Constant Coefficient of Variation
The Gamma Distribution
Models with Gamma-distributed Observations
Quasi-Likelihood Functions
Independent Observations
Dependent Observations
Optimal Estimating Functions
Optimality Criteria
Extended Quasi-Likelihood
Joint Modelling of Mean and Dispersion
Model Specification
Interaction between Mean and Dispersion Effects
Extended Quasi-Likelihood as a Criterion
Adjustments of the Estimating Equations
Joint Optimum Estimating Equations
Example: The Production of Leaf-Springs for Trucks
Models with Additional Non-Linear Parameters
Parameters in the Variance function
Parameters in the Link Function
Nonlinear Parameters in the Covariates
Model Checking
Techniqes in Model Checking
Score Tests for Extra Parameters
Smoothing as an Aid to Informal Checks
The Raw Materials of Model Checking
Checks for systematic Departure from Model
Check for isolated Departures from the Model
A Strategy for Model Checking?
Models for Survival Data
Proportional-Hazards Models
Estimation with a Specified Survival distribution
Example: Remission Times for Leukemia
Cox's Proportional-Hazards Model
Components of Dispersion
Linear Models
Nonlinear Models
Parameter Estimation
Example: A Salamander mating Experiment
Further Topics
Bias Adjustment
Computation of Bartlett Adjustments
Generalized Additive Models
Elementary Likelihood Theory
Edgeworth Series
Likelihood-Ratio Statistics
Index of Data Sets
Author Index
Subject Index
Each chapter also contains Bibliographic Notes and Exercises

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"... an important, useful book, well-written by two authorities in the field..."
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"... an enormous range of work is covered... represents, perhaps, the most important field of research in theoretical and practical statistics. For all statisticians working in this field, the book is essential."
-Short Book Reviews
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"... a definitive and unified the outstanding experts of this field."
"This is a wonderful book... Reading the book is like listening to a good lecturer. The authors present the material clearly, and they treat the reader with respect. There is a balance between discussion, mathematical presentation of models, and examples."

"... a complete introduction to the topic in a single monograph... a very readable book that provides the reader with great insight into a vast array of data analysis techniques...
-Siam Review

"... a unique and useful text for intermediate undergraduate teaching."